Problem: Simplify the following expression: ${4(-3y+1)-(-5-7y)}$
Explanation: Distribute the ${4}$ into the first set of parentheses: $ {4(}\gray{-3y+1}{)} - (-5-7y) $ $ {-12y+4} - (-5-7y) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ -12y+4 {-1(}\gray{-5-7y}{)} $ $ -12y+4 + {5+7y} $ Rewrite the expression to group the ${y}$ terms and numeric terms: $ {-12y + 7y} + {4 + 5}$ Combine the ${y}$ terms: $ {-5y} + {4 + 5}$ Combine the numeric terms: $ {-5y} + {9}$ The simplified expression is $-5y+9$